Integral representation of positive solutions of the heat equation

1984 ◽  
pp. 419-433 ◽  
Author(s):  
Bernard Mair ◽  
J. C. Taylor
Keyword(s):  
Integral Representation ◽  
Heat Equation ◽  
Positive Solutions

Gradient and Harnack-type estimates for PageRank

2020 ◽  
pp. 1-19
Author(s):  
Paul Horn ◽  
Lauren M. Nelsen
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Gradient Estimate ◽  
Personalized Pagerank ◽  
Geometric Properties ◽  
Algorithmic Design

Abstract Personalized PageRank has found many uses in not only the ranking of webpages, but also algorithmic design, due to its ability to capture certain geometric properties of networks. In this paper, we study the diffusion of PageRank: how varying the jumping (or teleportation) constant affects PageRank values. To this end, we prove a gradient estimate for PageRank, akin to the Li–Yau inequality for positive solutions to the heat equation (for manifolds, with later versions adapted to graphs).

scholarly journals Initial trace of positive solutions of a class of degenerate heat equation with absorption

2013 ◽  
Vol 33 (5) ◽  
pp. 2033-2063 ◽  
Author(s):  
Tai Nguyen Phuoc ◽  
◽  
Laurent Véron ◽  
Keyword(s):  
Heat Equation ◽  
Positive Solutions

Tail estimates for positive solutions of stochastic heat equation

Stochastics ◽  
2007 ◽  
Vol 79 (5) ◽  
pp. 407-417
Author(s):  
Habib Ouerdiane ◽  
José Luis da Silva
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Stochastic Heat Equation
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